We continue reading the paper on the design of high quality streaming proxy systems. We were reviewing Active prefetching. For a media content with uniform segmentation, we calculated the minimum buffer length to be the same in all three cases - the first segment, segments upto Bt/Bs and the segments thereafter. We also found the proxy jitter is unavoidable until the threshold.
We now do active pre-fetching for exponentially segmented object. Here we assume Bs  < twice Bt. the average rate of a specific segment is less than twice the average network bandwidth. When Bs >= 2 Bt, no prefetching of the uncached segments can be in time for the exponentially segmented objects.
For the case with no segment cached,  Proxy jitter in this case is inevitable.
For the case with the number of cached segments n to be between 0 and 1 + log-base-2( 1 / (2 - Bs/Bt)) threshold. The proxy starts to prefetch the next segment once the client starts to access this object. When the client accesses the segments between n+1 to the threshold, the proxy jitter becomes inevitable and the number of  and the minimum buffer size is the length of this segment at the threshold * Bt/Bs.

#codingexercise

GetAllNumberRangeSumCubeRootPowerFourteen) (Double [] A)

{

if (A == null) return 0;

Return A.AllNumberSumCubeRootPowerFourteen();

}

#codingexercise

GetAllNumberRangeProductCubeRootPowerSixteen) (Double [] A)

{

if (A == null) return 0;

Return A.AllNumberProductCubeRootPowerSixteen();

}